Question

A long solenoid of length $L$ has a mean diameter $D$. It has $n$ layers of winding of $N$ turns each. If it carries a current $i$, the magnetic field at its centre will be

• A. proportional to $D$
• B. inversely proportional to $D$
• C. independent of $D$
• D. proportional to $L$

Hint:

Magnetic field inside a long solenoid depends only on the number of turns per unit length and the current.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
For a long solenoid, $B = \mu_0 n i$, where $n$ is the number of turns per unit length.
Step 2: Detailed Explanation:
$n = \frac{\text{total turns}}{L} = \frac{n \times N}{L}$. This is independent of the diameter $D$.
Step 3: Final Answer:
The magnetic field is independent of $D$.